Subgroups — C₇₁×#61942 #31882814

Order 18176.

1762 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3399	C₂	1	4	yes	maximal, complemented
4	C₇₁×#3397	C₂	1	4	yes	maximal, complemented
5	C₇₁×#3376	C₂	1	4	yes	maximal, complemented
6	C₇₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₇₁×#3221	C₂	1	2	yes	maximal, complemented
8	C₇₁×#3220	C₂	1	2	yes	maximal, complemented
9	C₇₁×#3213	C₂	1	2	yes	maximal, complemented
10	C₇₁×#3126	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3122	C₂	1	2	yes	maximal, complemented
12	C₇₁×#3115	C₂	1	2	yes	maximal, complemented
13	C₇₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
14	#562×C₇₁	—	2	2	no	—
15	#559×C₇₁	C₂²	1	4	yes	—
16	#556×C₇₁	C₂²	1	4	yes	—
17	#554×C₇₁	C₂²	1	4	yes	complemented
18	#551×C₇₁	—	2	4	no	—
19	#550×C₇₁	C₂²	1	4	yes	complemented
20	#547×C₇₁	—	2	2	no	—
21	#542×C₇₁	—	2	2	no	—
22	#540×C₇₁	C₂²	1	2	yes	—
23	#540×C₇₁	C₂²	1	2	yes	—
24	#537×C₇₁	—	2	4	no	—
25	#536×C₇₁	C₂²	1	1	yes	characteristic
26	#535×C₇₁	C₂²	1	1	yes	characteristic
27	#533×C₇₁	C₂²	1	1	yes	characteristic
28	#532×C₇₁	C₂²	1	2	yes	—
29	#529×C₇₁	—	2	2	no	—
30	C₂×#124×C₇₁	C₂²	1	1	yes	characteristic
31	#519×C₇₁	C₂²	1	1	yes	characteristic
32	#518×C₇₁	C₂²	1	1	yes	characteristic
33	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
34	#496×C₇₁	C₂²	1	2	yes	—
35	#496×C₇₁	C₂²	1	4	yes	—
36	#496×C₇₁	C₂²	1	2	yes	complemented
37	#493×C₇₁	C₂²	1	2	yes	—
38	#492×C₇₁	C₂²	1	2	yes	complemented
39	#491×C₇₁	C₂²	1	2	yes	complemented
40	#490×C₇₁	C₂²	1	2	yes	—
41	#489×C₇₁	C₂²	1	4	yes	—
42	#488×C₇₁	C₂²	1	2	yes	—
43	#488×C₇₁	C₂²	1	2	yes	complemented
44	#482×C₇₁	C₂²	1	4	yes	—
45	#479×C₇₁	C₂²	1	4	yes	complemented
46	#478×C₇₁	C₂²	1	4	yes	—
47	#475×C₇₁	C₂²	1	2	yes	complemented
48	#474×C₇₁	C₂²	1	2	yes	complemented
49	#463×C₇₁	C₂²	1	4	yes	—
50	#463×C₇₁	C₂²	1	4	yes	—
51	#463×C₇₁	C₂²	1	4	yes	—
52	#463×C₇₁	C₂²	1	4	yes	complemented
53	#461×C₇₁	C₂²	1	4	yes	complemented
54	#460×C₇₁	C₂²	1	2	yes	complemented
55	#460×C₇₁	C₂²	1	4	yes	complemented
56	#459×C₇₁	C₂²	1	4	yes	—
57	#459×C₇₁	C₂²	1	4	yes	—
58	#459×C₇₁	C₂²	1	2	yes	complemented
59	#449×C₇₁	C₂²	1	4	yes	—
60	#448×C₇₁	C₂²	1	4	yes	—
61	#447×C₇₁	C₂²	1	4	yes	—
62	#446×C₇₁	C₂²	1	4	yes	complemented
63	#446×C₇₁	C₂²	1	4	yes	complemented
64	#442×C₇₁	C₂²	1	4	yes	—
65	#442×C₇₁	C₂²	1	4	yes	complemented
66	#440×C₇₁	C₂²	1	4	yes	complemented
67	#440×C₇₁	C₂²	1	4	yes	complemented
68	C₄×SD₁₆×C₇₁	C₂²	1	4	yes	complemented
69	C₄×D₈×C₇₁	C₂²	1	4	yes	—
70	#433×C₇₁	C₂²	1	2	yes	—
71	#433×C₇₁	C₂²	1	2	yes	—
72	#432×C₇₁	C₂²	1	2	yes	—
73	C₂×#41×C₇₁	—	2	4	no	—
74	C₂×#41×C₇₁	—	2	2	no	—
75	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
79	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
80	C₂×SD₁₆×C₇₁	C₂³	1	4	yes	—
81	C₂×D₈×C₇₁	C₂³	1	4	yes	—
82	C₂×D₈×C₇₁	C₂³	1	4	yes	—
83	C₂×D₈×C₇₁	C₂³	1	4	yes	—
84	C₄⋊Q₈×C₇₁	D₄	1	2	yes	—
85	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
87	#127×C₇₁	C₂³	1	2	yes	—
88	#127×C₇₁	C₂³	1	2	yes	—
89	#127×C₇₁	C₂³	1	2	yes	—
90	#127×C₇₁	C₂³	1	2	yes	—
91	#126×C₇₁	—	2	4	no	—
92	#126×C₇₁	—	2	4	no	—
93	#125×C₇₁	D₄	1	2	yes	—
94	#125×C₇₁	C₂³	1	2	yes	—
95	#125×C₇₁	C₂³	1	2	yes	—
96	#124×C₇₁	—	2	4	no	—
97	#124×C₇₁	—	2	1	no	—
98	#124×C₇₁	—	2	1	no	—
99	#124×C₇₁	—	2	2	no	—
100	#124×C₇₁	C₂³	1	2	yes	—
101	#124×C₇₁	C₂³	1	4	yes	—
102	#124×C₇₁	C₂³	1	2	yes	—
103	#123×C₇₁	—	2	4	no	—
104	#123×C₇₁	—	2	4	no	—
105	#123×C₇₁	—	2	4	no	—
106	#123×C₇₁	—	2	4	no	—
107	#123×C₇₁	—	2	2	no	—
108	C₂²⋊Q₈×C₇₁	—	2	4	no	—
109	C₂²⋊Q₈×C₇₁	—	2	4	no	—
110	C₂²⋊Q₈×C₇₁	—	2	2	no	—
111	C₂²⋊Q₈×C₇₁	—	2	4	no	—
112	C₂²⋊Q₈×C₇₁	—	2	4	no	—
113	C₂²⋊Q₈×C₇₁	D₄	1	4	yes	—
114	#121×C₇₁	—	2	2	no	—
115	#121×C₇₁	—	2	2	no	—
116	#121×C₇₁	—	2	4	no	—
117	#121×C₇₁	—	2	4	no	—
118	#121×C₇₁	—	2	4	no	—
119	#121×C₇₁	—	2	4	no	—
120	#121×C₇₁	—	2	4	no	—
121	#121×C₇₁	C₂³	1	4	yes	—
122	#120×C₇₁	—	2	2	no	—
123	C₄×Q₈×C₇₁	—	2	2	no	—
124	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
125	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
126	C₄×Q₈×C₇₁	C₂³	1	4	yes	—
127	C₄×D₄×C₇₁	—	2	2	no	—
128	C₄×D₄×C₇₁	—	2	2	no	—
129	C₄×D₄×C₇₁	—	2	4	no	—
130	C₄×D₄×C₇₁	—	2	2	no	—
131	C₄×D₄×C₇₁	C₂³	1	4	yes	—
132	C₄×D₄×C₇₁	C₂³	1	4	yes	—
133	C₄×D₄×C₇₁	C₂³	1	4	yes	—
134	C₄×D₄×C₇₁	C₂³	1	4	yes	—
135	C₄×D₄×C₇₁	C₂³	1	2	yes	—
136	#117×C₇₁	—	2	4	no	—
137	#117×C₇₁	—	2	2	no	—
138	#117×C₇₁	—	2	1	no	—
139	#117×C₇₁	C₂³	1	1	yes	characteristic
140	#117×C₇₁	C₂³	1	1	yes	characteristic
141	#117×C₇₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
145	C₂×C₄²×C₇₁	—	2	1	no	—
146	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
147	#107×C₇₁	C₂³	1	4	yes	—
148	#106×C₇₁	C₂³	1	4	yes	—
149	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
150	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
151	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
152	C₄⋊C₈×C₇₁	C₂³	1	4	yes	—
153	#103×C₇₁	C₂³	1	4	yes	—
154	#103×C₇₁	C₂³	1	4	yes	—
155	#103×C₇₁	C₂³	1	4	yes	—
156	#102×C₇₁	C₂³	1	4	yes	—
157	#102×C₇₁	C₂³	1	4	yes	—
158	#102×C₇₁	C₂³	1	4	yes	—
159	#102×C₇₁	C₂³	1	4	yes	—
160	#102×C₇₁	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₇₁	C₂³	1	4	yes	—
162	#97×C₇₁	C₂³	1	4	yes	—
163	#97×C₇₁	C₂³	1	2	yes	—
164	#97×C₇₁	C₂³	1	2	yes	—
165	C₄×C₈×C₇₁	C₂³	1	2	yes	—
166	C₄×C₈×C₇₁	C₂³	1	2	yes	—
167	C₂⁴×C₇₁	—	2	1	no	—
168	#41×C₇₁	—	4	2	no	—
169	#41×C₇₁	—	8	4	no	—
170	#41×C₇₁	—	8	8	no	—
171	C₂×Q₈×C₇₁	—	2	1	no	—
172	C₂×Q₈×C₇₁	—	2	2	no	—
173	C₂×Q₈×C₇₁	—	4	2	no	—
174	C₂×Q₈×C₇₁	C₂×D₄	1	4	yes	—
175	C₂×Q₈×C₇₁	C₂⁴	1	2	yes	—
176	C₂×Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
177	C₂×D₄×C₇₁	—	2	1	no	—
178	C₂×D₄×C₇₁	—	2	4	no	—
179	C₂×D₄×C₇₁	—	2	1	no	—
180	C₂×D₄×C₇₁	—	2	2	no	—
181	C₂×D₄×C₇₁	—	2	4	no	—
182	C₂×D₄×C₇₁	—	2	4	no	—
183	C₂×D₄×C₇₁	—	2	4	no	—
184	C₂×D₄×C₇₁	—	2	2	no	—
185	C₂×D₄×C₇₁	—	4	2	no	—
186	C₂×D₄×C₇₁	C₂⁴	1	2	yes	—
187	C₂×D₄×C₇₁	C₂⁴	1	1	yes	characteristic
188	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₇₁	—	2	1	no	—
190	C₂²×C₄×C₇₁	—	2	1	no	—
191	C₂²×C₄×C₇₁	—	2	4	no	—
192	C₂²×C₄×C₇₁	—	2	2	no	—
193	C₂²×C₄×C₇₁	—	2	4	no	—
194	C₂²×C₄×C₇₁	—	2	4	no	—
195	C₂²×C₄×C₇₁	—	2	4	no	—
196	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₇₁	—	4	4	no	—
199	SD₁₆×C₇₁	—	4	4	no	—
200	SD₁₆×C₇₁	—	4	4	no	—
201	D₈×C₇₁	—	4	4	no	—
202	D₈×C₇₁	—	4	4	no	—
203	D₈×C₇₁	—	4	4	no	—
204	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
205	C₂×C₈×C₇₁	C₂⁴	1	4	yes	—
206	C₄⋊C₄×C₇₁	—	2	2	no	—
207	C₄⋊C₄×C₇₁	—	2	4	no	—
208	C₄⋊C₄×C₇₁	—	2	4	no	—
209	C₄⋊C₄×C₇₁	—	2	2	no	—
210	C₄⋊C₄×C₇₁	—	2	4	no	—
211	C₄⋊C₄×C₇₁	—	2	4	no	—
212	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
213	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
217	C₄⋊C₄×C₇₁	C₂⁴	1	2	yes	—
218	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
219	C₂²⋊C₄×C₇₁	—	2	1	no	—
220	C₂²⋊C₄×C₇₁	—	2	4	no	—
221	C₂²⋊C₄×C₇₁	—	2	4	no	—
222	C₂²⋊C₄×C₇₁	—	2	4	no	—
223	C₂²⋊C₄×C₇₁	—	2	2	no	—
224	C₂²⋊C₄×C₇₁	—	2	4	no	—
225	C₂²⋊C₄×C₇₁	—	2	4	no	—
226	C₂²⋊C₄×C₇₁	—	2	4	no	—
227	C₂²⋊C₄×C₇₁	—	2	4	no	—
228	C₂²⋊C₄×C₇₁	—	2	4	no	—
229	C₂²⋊C₄×C₇₁	—	2	4	no	—
230	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
232	C₄²×C₇₁	—	2	2	no	—
233	C₄²×C₇₁	—	2	1	no	—
234	C₄²×C₇₁	—	2	4	no	—
235	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₇₁	C₂⁴	1	2	yes	—
238	C₄²×C₇₁	C₂⁴	1	2	yes	—
239	C₄²×C₇₁	C₂⁴	1	2	yes	—
240	C₂³×C₇₁	—	2	2	no	—
241	C₂³×C₇₁	—	2	1	no	—
242	C₂³×C₇₁	—	2	4	no	—
243	C₂³×C₇₁	—	4	2	no	—
244	C₂³×C₇₁	—	8	2	no	—
245	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₇₁	—	2	4	no	—
247	Q₈×C₇₁	—	2	2	no	—
248	Q₈×C₇₁	—	4	4	no	—
249	Q₈×C₇₁	—	4	2	no	—
250	Q₈×C₇₁	—	8	2	no	—
251	D₄×C₇₁	—	2	4	no	—
252	D₄×C₇₁	—	2	4	no	—
253	D₄×C₇₁	—	2	2	no	—
254	D₄×C₇₁	—	2	4	no	—
255	D₄×C₇₁	—	4	2	no	—
256	D₄×C₇₁	—	4	4	no	—
257	D₄×C₇₁	—	4	2	no	—
258	D₄×C₇₁	—	8	4	no	—
259	D₄×C₇₁	—	8	2	no	—
260	D₄×C₇₁	—	8	4	no	—
261	D₄×C₇₁	—	8	4	no	—
262	D₄×C₇₁	—	8	4	no	—
263	C₂×C₄×C₇₁	—	2	2	no	—
264	C₂×C₄×C₇₁	—	2	2	no	—
265	C₂×C₄×C₇₁	—	2	2	no	—
266	C₂×C₄×C₇₁	—	2	1	no	—
267	C₂×C₄×C₇₁	—	2	4	no	—
268	C₂×C₄×C₇₁	—	4	2	no	—
269	C₂×C₄×C₇₁	—	4	2	no	—
270	C₂×C₄×C₇₁	—	4	8	no	—
271	C₂×C₄×C₇₁	—	4	2	no	—
272	C₂×C₄×C₇₁	—	8	2	no	—
273	C₂×C₄×C₇₁	—	8	4	no	—
274	C₂×C₄×C₇₁	—	8	4	no	—
275	C₂×C₄×C₇₁	—	8	4	no	—
276	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
282	C₈×C₇₁	—	2	4	no	—
283	C₈×C₇₁	—	2	4	no	—
284	C₂²×C₇₁	—	2	2	no	—
285	C₂²×C₇₁	—	2	1	no	—
286	C₂²×C₇₁	—	4	4	no	—
287	C₂²×C₇₁	—	4	4	no	—
288	C₂²×C₇₁	—	4	2	no	—
289	C₂²×C₇₁	—	4	4	no	—
290	C₂²×C₇₁	—	4	1	no	—
291	C₂²×C₇₁	—	4	2	no	—
292	C₂²×C₇₁	—	4	4	no	—
293	C₂²×C₇₁	—	16	2	no	—
294	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₇₁	—	2	2	no	—
296	C₄×C₇₁	—	2	2	no	—
297	C₄×C₇₁	—	2	4	no	—
298	C₄×C₇₁	—	2	4	no	—
299	C₄×C₇₁	—	2	1	no	—
300	C₄×C₇₁	—	4	4	no	—
301	C₄×C₇₁	—	4	2	no	—
302	C₄×C₇₁	—	4	1	no	—
303	C₄×C₇₁	—	4	2	no	—
304	C₄×C₇₁	#585	1	2	yes	—
305	#61942	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂×C₇₁	—	4	1	no	—
307	C₂×C₇₁	—	8	4	no	—
308	C₂×C₇₁	—	8	1	no	—
309	C₂×C₇₁	—	8	2	no	—
310	C₂×C₇₁	#3487	1	1	yes	characteristic
311	C₂×C₇₁	#3585	1	2	yes	—
312	#3548	C₂×C₇₁	1	1	yes	characteristic, complemented
313	#3510	C₂×C₇₁	1	1	yes	characteristic, complemented
314	#3399	C₂×C₇₁	1	4	yes	complemented
315	#3397	C₂×C₇₁	1	4	yes	complemented
316	#3376	C₂×C₇₁	1	4	yes	complemented
317	#3370	C₂×C₇₁	1	4	yes	complemented
318	#3221	C₂×C₇₁	1	2	yes	complemented
319	#3220	C₂×C₇₁	1	2	yes	complemented
320	#3213	C₂×C₇₁	1	2	yes	complemented
321	#3126	C₂×C₇₁	1	2	yes	complemented
322	#3122	C₂×C₇₁	1	2	yes	complemented
323	#3115	C₂×C₇₁	1	2	yes	complemented
324	#2987	C₂×C₇₁	1	1	yes	characteristic, complemented
325	C₇₁	#61942	1	1	yes	characteristic, direct product factor, Sylow
326	#562	—	2	2	no	—
327	#559	C₂²×C₇₁	1	4	yes	—
328	#556	C₂²×C₇₁	1	4	yes	—
329	#554	C₂²×C₇₁	1	4	yes	complemented
330	#551	—	2	4	no	—
331	#550	C₂²×C₇₁	1	4	yes	complemented
332	#547	—	2	2	no	—
333	#542	—	2	2	no	—
334	#540	C₂²×C₇₁	1	2	yes	—
335	#540	C₂²×C₇₁	1	2	yes	—
336	#537	—	2	4	no	—
337	#536	C₂²×C₇₁	1	1	yes	characteristic
338	#535	C₂²×C₇₁	1	1	yes	characteristic
339	#533	C₂²×C₇₁	1	1	yes	characteristic
340	#532	C₂²×C₇₁	1	2	yes	—
341	#529	—	2	2	no	—
342	C₂×#124	C₂²×C₇₁	1	1	yes	characteristic
343	#519	C₂²×C₇₁	1	1	yes	characteristic
344	#518	C₂²×C₇₁	1	1	yes	characteristic
345	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
346	#496	C₂²×C₇₁	1	2	yes	—
347	#496	C₂²×C₇₁	1	4	yes	—
348	#496	C₂²×C₇₁	1	2	yes	complemented
349	#493	C₂²×C₇₁	1	2	yes	—
350	#492	C₂²×C₇₁	1	2	yes	complemented
351	#491	C₂²×C₇₁	1	2	yes	complemented
352	#490	C₂²×C₇₁	1	2	yes	—
353	#489	C₂²×C₇₁	1	4	yes	—
354	#488	C₂²×C₇₁	1	2	yes	—
355	#488	C₂²×C₇₁	1	2	yes	complemented
356	#482	C₂²×C₇₁	1	4	yes	—
357	#479	C₂²×C₇₁	1	4	yes	complemented
358	#478	C₂²×C₇₁	1	4	yes	—
359	#475	C₂²×C₇₁	1	2	yes	complemented
360	#474	C₂²×C₇₁	1	2	yes	complemented
361	#463	C₂²×C₇₁	1	4	yes	—
362	#463	C₂²×C₇₁	1	4	yes	—
363	#463	C₂²×C₇₁	1	4	yes	—
364	#463	C₂²×C₇₁	1	4	yes	complemented
365	#461	C₂²×C₇₁	1	4	yes	complemented
366	#460	C₂²×C₇₁	1	2	yes	complemented
367	#460	C₂²×C₇₁	1	4	yes	complemented
368	#459	C₂²×C₇₁	1	4	yes	—
369	#459	C₂²×C₇₁	1	4	yes	—
370	#459	C₂²×C₇₁	1	2	yes	complemented
371	#449	C₂²×C₇₁	1	4	yes	—
372	#448	C₂²×C₇₁	1	4	yes	—
373	#447	C₂²×C₇₁	1	4	yes	—
374	#446	C₂²×C₇₁	1	4	yes	complemented
375	#446	C₂²×C₇₁	1	4	yes	complemented
376	#442	C₂²×C₇₁	1	4	yes	—
377	#442	C₂²×C₇₁	1	4	yes	complemented
378	#440	C₂²×C₇₁	1	4	yes	complemented
379	#440	C₂²×C₇₁	1	4	yes	complemented
380	C₄×SD₁₆	C₂²×C₇₁	1	4	yes	complemented
381	C₄×D₈	C₂²×C₇₁	1	4	yes	—
382	#433	C₂²×C₇₁	1	2	yes	—
383	#433	C₂²×C₇₁	1	2	yes	—
384	#432	C₂²×C₇₁	1	2	yes	—
385	C₂×#41	—	2	4	no	—
386	C₂×#41	—	2	2	no	—
387	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
389	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
390	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
391	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
392	C₂×SD₁₆	C₂³×C₇₁	1	4	yes	—
393	C₂×D₈	C₂³×C₇₁	1	4	yes	—
394	C₂×D₈	C₂³×C₇₁	1	4	yes	—
395	C₂×D₈	C₂³×C₇₁	1	4	yes	—
396	C₄⋊Q₈	D₄×C₇₁	1	2	yes	—
397	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
398	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
399	#127	C₂³×C₇₁	1	2	yes	—
400	#127	C₂³×C₇₁	1	2	yes	—
401	#127	C₂³×C₇₁	1	2	yes	—
402	#127	C₂³×C₇₁	1	2	yes	—
403	#126	—	2	4	no	—
404	#126	—	2	4	no	—
405	#125	D₄×C₇₁	1	2	yes	—
406	#125	C₂³×C₇₁	1	2	yes	—
407	#125	C₂³×C₇₁	1	2	yes	—
408	#124	—	2	4	no	—
409	#124	—	2	1	no	—
410	#124	—	2	1	no	—
411	#124	—	2	2	no	—
412	#124	C₂³×C₇₁	1	4	yes	—
413	#124	C₂³×C₇₁	1	2	yes	—
414	#124	C₂³×C₇₁	1	2	yes	—
415	#123	—	2	4	no	—
416	#123	—	2	4	no	—
417	#123	—	2	4	no	—
418	#123	—	2	4	no	—
419	#123	—	2	2	no	—
420	C₂²⋊Q₈	—	2	4	no	—
421	C₂²⋊Q₈	—	2	4	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	4	no	—
424	C₂²⋊Q₈	—	2	4	no	—
425	C₂²⋊Q₈	D₄×C₇₁	1	4	yes	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	4	no	—
429	#121	—	2	4	no	—
430	#121	—	2	4	no	—
431	#121	—	2	4	no	—
432	#121	—	2	4	no	—
433	#121	C₂³×C₇₁	1	4	yes	—
434	#120	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
437	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
438	C₄×Q₈	C₂³×C₇₁	1	4	yes	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	C₂³×C₇₁	1	2	yes	—
444	C₄×D₄	C₂³×C₇₁	1	4	yes	—
445	C₄×D₄	C₂³×C₇₁	1	4	yes	—
446	C₄×D₄	C₂³×C₇₁	1	4	yes	—
447	C₄×D₄	C₂³×C₇₁	1	4	yes	—
448	#117	—	2	4	no	—
449	#117	—	2	2	no	—
450	#117	—	2	1	no	—
451	#117	C₂³×C₇₁	1	1	yes	characteristic
452	#117	C₂³×C₇₁	1	1	yes	characteristic
453	#117	C₂³×C₇₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₂²⋊C₄	—	2	2	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
459	#107	C₂³×C₇₁	1	4	yes	—
460	#106	C₂³×C₇₁	1	4	yes	—
461	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
462	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
463	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
464	C₄⋊C₈	C₂³×C₇₁	1	4	yes	—
465	#103	C₂³×C₇₁	1	4	yes	—
466	#103	C₂³×C₇₁	1	4	yes	—
467	#103	C₂³×C₇₁	1	4	yes	—
468	#102	C₂³×C₇₁	1	4	yes	—
469	#102	C₂³×C₇₁	1	4	yes	—
470	#102	C₂³×C₇₁	1	4	yes	—
471	#102	C₂³×C₇₁	1	4	yes	—
472	#102	C₂³×C₇₁	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₇₁	1	4	yes	—
474	#97	C₂³×C₇₁	1	4	yes	—
475	#97	C₂³×C₇₁	1	2	yes	—
476	#97	C₂³×C₇₁	1	2	yes	—
477	C₄×C₈	C₂³×C₇₁	1	2	yes	—
478	C₄×C₈	C₂³×C₇₁	1	2	yes	—
479	C₂⁴	—	2	1	no	—
480	#41	—	4	2	no	—
481	#41	—	8	4	no	—
482	#41	—	8	8	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	4	2	no	—
486	C₂×Q₈	C₂×D₄×C₇₁	1	4	yes	—
487	C₂×Q₈	C₂⁴×C₇₁	1	2	yes	—
488	C₂×Q₈	C₂⁴×C₇₁	1	1	yes	characteristic
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	C₂⁴×C₇₁	1	2	yes	—
499	C₂×D₄	C₂⁴×C₇₁	1	1	yes	characteristic
500	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	4	4	no	—
512	SD₁₆	—	4	4	no	—
513	D₈	—	4	4	no	—
514	D₈	—	4	4	no	—
515	D₈	—	4	4	no	—
516	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
517	C₂×C₈	C₂⁴×C₇₁	1	4	yes	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
525	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
526	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
527	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
528	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
529	C₄⋊C₄	C₂⁴×C₇₁	1	2	yes	—
530	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
543	C₂²⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	4	no	—
547	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
549	C₄²	C₂⁴×C₇₁	1	2	yes	—
550	C₄²	C₂⁴×C₇₁	1	2	yes	—
551	C₄²	C₂⁴×C₇₁	1	2	yes	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
558	Q₈	—	2	4	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	4	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	8	2	no	—
571	D₄	—	8	4	no	—
572	D₄	—	8	4	no	—
573	D₄	—	8	4	no	—
574	D₄	—	8	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	8	4	no	—
585	C₂×C₄	—	8	4	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
591	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
593	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	2	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	16	2	no	—
606	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	4	no	—
611	C₄	—	2	1	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	#585×C₇₁	1	2	yes	—
617	C₂	—	4	1	no	—
618	C₂	—	8	2	no	—
619	C₂	—	8	4	no	—
620	C₂	—	8	1	no	—
621	C₂	C₇₁×#3487	1	1	yes	characteristic
622	C₂	C₇₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ #533×C₇₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇₁×#3548	C₂	semidirect
2. C₇₁×#3510	C₂	semidirect
3. C₇₁×#3399	C₂	semidirect
4. C₇₁×#3397	C₂	semidirect
5. C₇₁×#3376	C₂	semidirect
6. C₇₁×#3370	C₂	semidirect
7. C₇₁×#3221	C₂	semidirect
8. C₇₁×#3220	C₂	semidirect
9. C₇₁×#3213	C₂	semidirect
10. C₇₁×#3126	C₂	semidirect
11. C₇₁×#3122	C₂	semidirect
12. C₇₁×#3115	C₂	semidirect
13. C₇₁×#2987	C₂	semidirect
17. #554×C₇₁	C₂²	semidirect
19. #550×C₇₁	C₂²	semidirect
36. #496×C₇₁	C₂²	semidirect
38. #492×C₇₁	C₂²	semidirect
39. #491×C₇₁	C₂²	semidirect
43. #488×C₇₁	C₂²	semidirect
45. #479×C₇₁	C₂²	semidirect
47. #475×C₇₁	C₂²	semidirect
48. #474×C₇₁	C₂²	semidirect
52. #463×C₇₁	C₂²	semidirect
53. #461×C₇₁	C₂²	semidirect
54. #460×C₇₁	C₂²	semidirect
55. #460×C₇₁	C₂²	semidirect
58. #459×C₇₁	C₂²	semidirect
62. #446×C₇₁	C₂²	semidirect
63. #446×C₇₁	C₂²	semidirect
65. #442×C₇₁	C₂²	semidirect
66. #440×C₇₁	C₂²	semidirect
67. #440×C₇₁	C₂²	semidirect
68. C₄×SD₁₆×C₇₁	C₂²	semidirect
305. #61942	C₇₁	direct (N × H)
312. #3548	C₂×C₇₁	semidirect
313. #3510	C₂×C₇₁	semidirect
314. #3399	C₂×C₇₁	semidirect
315. #3397	C₂×C₇₁	semidirect
316. #3376	C₂×C₇₁	semidirect
317. #3370	C₂×C₇₁	semidirect
318. #3221	C₂×C₇₁	semidirect
319. #3220	C₂×C₇₁	semidirect
320. #3213	C₂×C₇₁	semidirect
321. #3126	C₂×C₇₁	semidirect
322. #3122	C₂×C₇₁	semidirect
323. #3115	C₂×C₇₁	semidirect
324. #2987	C₂×C₇₁	semidirect
325. C₇₁	#61942	direct (N × H)
329. #554	C₂²×C₇₁	semidirect
331. #550	C₂²×C₇₁	semidirect
348. #496	C₂²×C₇₁	semidirect
350. #492	C₂²×C₇₁	semidirect
351. #491	C₂²×C₇₁	semidirect
355. #488	C₂²×C₇₁	semidirect
357. #479	C₂²×C₇₁	semidirect
359. #475	C₂²×C₇₁	semidirect
360. #474	C₂²×C₇₁	semidirect
364. #463	C₂²×C₇₁	semidirect
365. #461	C₂²×C₇₁	semidirect
366. #460	C₂²×C₇₁	semidirect
367. #460	C₂²×C₇₁	semidirect
370. #459	C₂²×C₇₁	semidirect
374. #446	C₂²×C₇₁	semidirect
375. #446	C₂²×C₇₁	semidirect
377. #442	C₂²×C₇₁	semidirect
378. #440	C₂²×C₇₁	semidirect
379. #440	C₂²×C₇₁	semidirect
380. C₄×SD₁₆	C₂²×C₇₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇₁×#3548	2
C₇₁×#3510	2
C₇₁×#3399	2
C₇₁×#3397	2
C₇₁×#3376	2
C₇₁×#3370	2
C₇₁×#3221	2
C₇₁×#3220	2
C₇₁×#3213	2
C₇₁×#3126	2
C₇₁×#3122	2
C₇₁×#3115	2
C₇₁×#2987	2
#61942	71

Subgroups — C71×#61942 #31882814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#61942 #31882814